Question

use minitab to solve/

Box and Liu describe an experiment flying paper helicopters where the objective is to maximize flight

time. They used the central composite design shown in Table below. Each run involved a single helicopter made to the following specifications: x1 = wing area (in2), -1 = 11.80 and +1 = 13.00; x2 = wing-length to width ratio, -1 = 2.25 and +1 = 2.78; x3 = base width (in), -1 = 1.00 and +1 = 1.50; and x4 = base length (in), -1 = 1.50 and +1 = 2.50. Each helicopter was flown four times and the average flight time and the standard deviation of flight time was recorded.

(a) Fit a second-order model to the average flight time response.

(b) Fit a second-order model to the standard deviation of flight time response.

(c) Analyze the residuals for both models from parts (a) and (b). Are transformations on the response(s) necessary? If so, fit the appropriate models.

(d) What design would you recommend to maximize the flight time?

(e) What design would you recommend to maximize the flight time while simultaneously minimizing the standard deviation of flight time?

This question is from the Industrial Engineering and uses a mini-tab to solve it

Answer 1

Solution:

Design Expert Output

Response 1                        Avg Fit Time

ANOVA for response surface reduced quadartic model

Analysis of variance table [Partial sum of squares - Type III]

Source	Sum of squares	df	Mean square	F value	P-value Prob >F
Model	0.28	11	0.025	15.78	<0.0001 significance
A-wing area	1.67E005	1	1.667E005	0.010	0.9198
B length width	0.062	1	0.062	38.83	<0.0001
Cbase width	1.500E004	1	1.500E004	0.094	0.7628
Dbase width	0.089	1	0.089	55.61	<0.0001
AB	0.013	1	0.013	8.28	0.0100
AC	0.023	1	0.023	14.09	0.0015
AD	0.031	1	0.031	19.17	0.0004
BC	0.034	1	0.034	21.43	0.0002
CD	7.225E003	1	7.22E003	4.52	0.0475
A2	7.511E003	1	7.51E003	4.70	0.0438
C2	0.013	1	0.013	8.04	0.0110
Residual	0.029	18	1.597E003
LACK OF FIT	0.020	13	1.513E003	0.83	0.6382
PURE ERROR	9.083E003	5
COR TOTAL	0.31	29

Std. dev 0.040           R squared    0.9060

mean   3.66                Adj R-squared 0.8486

c.v% 1.09                    Pred R squared 0.7581

press 0.074                   Adeq predision   19.913

Factor	Coefficient Estimate	df	Standard Error	95%CI Low	95%CI High	VIF
INTERCEPT	370	1	0.012	367	372	1.00
a wing area	8.33E004	1	8.158E003	0.018	0.016	1.00
B length width	0.051	1	8.158E003	0.034	0.068	1.00
C Base width	2.500E003	1	8.158E003	0.015	0.020	1.00
D base width	0.061	1	8.158E003	0.078	0.054	1.00
AB	0.029	1	9.991E003	0.050	7.75E003	1.00
AC	0.037	1	9.991E003	0.058	0.017	1.00
AD	0.044	1	9.991E003	0.023	0.065	1.00
BC	0.045	1	9.991E003	0.025	0.067	1.00
CD	0.021	1	9.991E003	0.042	2.590E004	1.00
A2	0.016	1	7.491E003	0.032	5.060E004	1.01
C2	0.021	1	1.491E003	0.037	5.507E003	1.01

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Thank you.